I was going to suggest, that I really don't see how you can apply the same mathematical formulas to collectively explain the behavior of the universe and such. It didn't even start out that way, it started out as Metaphysics which was not math heavy.
No factor can be the same, and it seems like Mathematics tries to explain everything as a constant. Like individuals and groups, you cannot account group behavior for every individual. I don't see how you can factor the entire universe for every little physical thing and movement.
I was going to read Stephen Hawking's "A History of Time", it is supposed to explain the major physics of concepts without being math heavy at all.
The difference between economics and sciences such as physics and biology is economics is a social science, and as such is more comparable to anthropology, sociology, history, etc.
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Democracy for Breakfast: No factor can be the same, and it seems like Mathematics tries to explain everything as a constant.
No factor can be the same, and it seems like Mathematics tries to explain everything as a constant.
Looks like I studied time dependent differential equations for nothing!
More seriously, I think it is key to understand the differences in the methodological pinnings of both the social sciences and the natural sciences. The principle factor assumed a priori and without which physical theories cease to contain any meaning without is causality, and therefore the principle of being able to isolate phenomena and reason from induction with or without the effects of their existence. It is an imperfect process of induction requiring both careful observation and reasoning. One of the most wonderous discoveries of mankind has been to find through this method how elegantly mathematics, a creation of the human mind serves as a tool of description for the natural world, even though mathematics itself is an prioriistic deductive discipline.
In the social realm, in so far as we may reason teleologically that ourselves and other individuals act and are reasoning human beings, the rejection of which soon runs into horrible contradictions like the positivist claiming we cannot claim others reason like us while attempting to appeal to this uniformity of reasoning in order to advance his case, etc. Since we may arrive at the theorems of praxeology by reasoning upon the concept of action, since action is the well spring of reason, and we ourselves are acting beings, and in so far we recognise and cannot reasonably deny that others are too; our theorems begin to have synthetic truth in describing the actions taken in the real world and can bring real knowledge about the consequences of actions that are brought to tangible reality through the application of tangible, real means towards the application mental and perceived ends.Interpretation of empirical phenomena requires an establishment of the level to which conditions where the praxeological theorems apply however, and the way in which these statements are stated "all other things being equal", thereby entails their practical applicatio requires awareness of the levels of changes in all variables in order to sort out the different effects and prevent errors in inference.
In this sense, we may consider mathematics and praxeology to have a curious parallel relationship with regard to the disciplines of physics and history respectively.
You are correct that Physics has given up the task of prediction of all phenomena in exact terms, both theoretically and from what may be considered possible from a human perspective and these limits have been found in both quantum mechanics and the theory of chaos in different respects. These inferences have come about as a result of the methods applied to Physics and not "from without", taking some vague notion from another discipline.
Similiarly, the limitations brought about towards economic calculation and rational allocation in multiple stage production systems is a realisation purely grounded in praxeological reasoning, and such knowledge as evidenced by Mises cannot be achieved by attempting to ape the methods of the natural sciences.
Hope that helped!
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Democracy for Breakfast: I was going to suggest, that I really don't see how you can apply the same mathematical formulas to collectively explain the behavior of the universe and such. Math can do a great job when dealing with any number of individuals, innumerable trillions and trillions of them, provided the little tykes are interchangable. So it can find out all kinds of stuff about atoms and such like. There is indeed a calculation problem trying to figure out what any individual atom will do, but the great laws of probability and statistics can say something about what the great mass of them will be doing. One example that impressed me is that given the statistics of a dangerous road, one can say something like "There is a 95% chance that there will be at least 300 accidents on this road this year,even though we can't say which car and driver will be in an accident." It didn't even start out that way, it started out as Metaphysics which was not math heavy. No factor can be the same, and it seems like Mathematics tries to explain everything as a constant. I'm not sure what you mean here. Indeed Math works best [only?] if the differences between individuals can be ignored. In the road accident example, although every driver is completely different, the road seems to be such that the differences in drivers doesn't mean much and can be ignored. Like individuals and groups, you cannot account group behavior for every individual. That's the great beauty and wonder of statistics, that it can predict a lot about the behavior of a group, even though it can't say anything about the individual. I'm reminded for some reason of that evil genius, Adolf Hitler. He had tremendous insight on how to deal with crowds, how to excite and influence them, and he published some of it. I imagine that he understood that the differences between people can be ignored when subjected to the powerful forces he was able to unleash with his speeches and tricks. I don't see how you can factor the entire universe for every little physical thing and movement. You can't. But you can still know alot about the universe as a whole. I was going to read Stephen Hawking's "A History of Time", it is supposed to explain the major physics of concepts without being math heavy at all. I was quite jealous when I read that book. Here he is, having a great time playing with ideas, and getting fame and fortune for it.
I was going to suggest, that I really don't see how you can apply the same mathematical formulas to collectively explain the behavior of the universe and such.
Math can do a great job when dealing with any number of individuals, innumerable trillions and trillions of them, provided the little tykes are interchangable. So it can find out all kinds of stuff about atoms and such like. There is indeed a calculation problem trying to figure out what any individual atom will do, but the great laws of probability and statistics can say something about what the great mass of them will be doing.
One example that impressed me is that given the statistics of a dangerous road, one can say something like "There is a 95% chance that there will be at least 300 accidents on this road this year,even though we can't say which car and driver will be in an accident."
It didn't even start out that way, it started out as Metaphysics which was not math heavy.
I'm not sure what you mean here. Indeed Math works best [only?] if the differences between individuals can be ignored. In the road accident example, although every driver is completely different, the road seems to be such that the differences in drivers doesn't mean much and can be ignored.
Like individuals and groups, you cannot account group behavior for every individual.
That's the great beauty and wonder of statistics, that it can predict a lot about the behavior of a group, even though it can't say anything about the individual.
I'm reminded for some reason of that evil genius, Adolf Hitler. He had tremendous insight on how to deal with crowds, how to excite and influence them, and he published some of it. I imagine that he understood that the differences between people can be ignored when subjected to the powerful forces he was able to unleash with his speeches and tricks.
I don't see how you can factor the entire universe for every little physical thing and movement.
You can't. But you can still know alot about the universe as a whole.
I was quite jealous when I read that book. Here he is, having a great time playing with ideas, and getting fame and fortune for it.
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You guys sound so enthusiastic about Math. I was really bored by Math in High School and never really good at it, and now even in College I can't stand it. Is reasoning possible without mathematics?
Democracy for Breakfast:I really don't see how you can apply the same mathematical formulas to collectively explain the behavior of the universe and such.
http://en.wikipedia.org/wiki/COBE
Liking something as an end in itself and realising its utillity as a means can be entirely different things. Mathematics can be applied to reason about the real world, just like praxeology and logic when the assumptions underlying its statements are valid.
Admittedly, I have gone from disdaining mathematics when I was younger to admiring it now, though this has taken time and familiarising myself with it. This has partly come about with the way I began to study it more and more independently over time.
I must also confess, I see no real elegance to most of the mathematics I see applied in the social sciences, in fact it gives me a headache, though this is a side point...
Smiling Dave: One example that impressed me is that given the statistics of a dangerous road, one can say something like "There is a 95% chance that there will be at least 300 accidents on this road this year,even though we can't say which car and driver will be in an accident."
Yeah but. To the extent that that prediction is published (say you put a billboard on each end of the road), what effect does that have on the results
Seems to me that is a good example of basic difference between praxeology vs natural sciences.
For the past few weeks, I've been spending some time thinking about how I can apply free market principles to problems in computer science. Nothing great has come up yet, but I'll figure out something.
johnclonts: Smiling Dave: One example that impressed me is that given the statistics of a dangerous road, one can say something like "There is a 95% chance that there will be at least 300 accidents on this road this year,even though we can't say which car and driver will be in an accident." Yeah but. To the extent that that prediction is published (say you put a billboard on each end of the road), what effect does that have on the results Depends on what the problem is with the road. If its full of curvy slippery dangerous icy spots right next to a cliff, well people know it's dangerous already. The thing probably has a reputation with the locals. But that won't change the basic power of the Math to predict accirately that 300 people will die, but certainly it can't say in advance who they will be. Seems to me that is a good example of basic difference between praxeology vs natural sciences. I don't understand what you mean, could you kindly explain?
Depends on what the problem is with the road. If its full of curvy slippery dangerous icy spots right next to a cliff, well people know it's dangerous already. The thing probably has a reputation with the locals. But that won't change the basic power of the Math to predict accirately that 300 people will die, but certainly it can't say in advance who they will be.
I don't understand what you mean, could you kindly explain?
Democracy for Breakfast: You guys sound so enthusiastic about Math. I was really bored by Math in High School and never really good at it, and now even in College I can't stand it. Is reasoning possible without mathematics? Of course it is. Winston Churchill was a pretty smart fellow by all accounts, and he had no talent for Math, and indeed hated it. Malcolm X strikes me as a very intelligent guy, but he had no clue when it came to Math, as his autobiography tells us. I'm sure the list can be expanded greatly. One thing is important when it comes to reasoning, and that is finding out what makes up a logical argument, what are the typical logical fallacies, that kind of thing. I personally was very educated by a book called the Art of Clear Thinking, by Rudolf Flesch, though I'm sure there are other sources for that kind of info.
Of course it is. Winston Churchill was a pretty smart fellow by all accounts, and he had no talent for Math, and indeed hated it.
Malcolm X strikes me as a very intelligent guy, but he had no clue when it came to Math, as his autobiography tells us.
I'm sure the list can be expanded greatly.
One thing is important when it comes to reasoning, and that is finding out what makes up a logical argument, what are the typical logical fallacies, that kind of thing. I personally was very educated by a book called the Art of Clear Thinking, by Rudolf Flesch, though I'm sure there are other sources for that kind of info.
Smiling Dave:Depends on what the problem is with the road. If its full of curvy slippery dangerous icy spots right next to a cliff, well people know it's dangerous already. The thing probably has a reputation with the locals. But that won't change the basic power of the Math to predict accirately that 300 people will die, but certainly it can't say in advance who they will be.
Depends, if you know which people are the worse drivers and the best drivers, you can use probability.
@ the OP
The physical universe can be represented mathematically b/c it is governed by time-invariant operating causes. Also, hawking is an idiot propped up on stilts.
>I was going to suggest, that I really don't see how you can apply the same mathematical formulas to collectively explain the behavior of the universe and such
Well, you CAN explain the universe reliably with math. At least, we can do a lot now (like creating microchips and fusion weapons) and we keep getting better. My guess is that math is so effective because the universe literally is nothing more than a mathematical system (set of axioms). In practice, though, things (like with psychology, economics, sociology climatology, medicine) cannot be "solved" with math or physics. There are too many variables, too much interaction, and too many measurements that would have to be made to obtain precise solutions. You can't practically measure the state of every atom or neuron in a human brain and predict it's behavior computationally; you have to use things like praxeology instead. This is a limitation of mankind and not a limitation of mathematics: in Human Action, even Mises admits the possibility that some kind of superbeing could precisely predict the behavior of a man.
>It didn't even start out that way, it started out as Metaphysics which was not math heavy.
I don't know at all what you mean by "Metaphysics".
>I was going to read Stephen Hawking's "A History of Time", it is supposed to explain the major physics of concepts without being math heavy at all.
If you want an enjoyable read, I suggest The Five Ages of the Universe. It talks about real science but also does some fun stuff like conjecture what the universe will be like 1 trillion years from now. It gets your imagination going, which Hawking's books do not IMHO.
Smiling Dave: Seems to me that is a good example of basic difference between praxeology vs natural sciences. I don't understand what you mean, could you kindly explain?
My point was that publishing the results ( that statistically 300 people will die on the road) will likely cause drivers to act differently than they would otherwise, thus changing the basis upon which the results were computed. This is different than in the natural sciences. Because Humans Act. Trees don't act, projectiles don't act, etc.
Democracy for Breakfast: I was going to read Stephen Hawking's "A History of Time", it is supposed to explain the major physics of concepts without being math heavy at all.
Considering that I read it when I was 11, that is a safe assessment.
You kids need to read A New Kind of Science.
The fallacies of intellectual communism, a compilation - On the nature of power
Stranger: You kids need to read A New Kind of Science.
That helps with evolution.
Additionally, what are some good books to read on the Natural Sciences? something intellectually stimulating, or presents important theories/problems really well.
Or, easy to understand books on Physics, and all its important theories.
Democracy for Breakfast: Or, easy to understand books on Physics, and all its important theories.
This doesn't cover the 20th century, but believe me that's still a hell of a lot. Actually along with Human Action and another book I think it's been the most influential in my intellectual development:
Mathematics and the Physical World by Morris Kline
The calculation problem is only a problem in the case of values. The universe is more of a deciphering complexity problem.
I'm interested in building some models, are there any I should look into buying? Or nice display models to do with Physics,Astronomy or Calc?